File:ArcTaniaMap70.png

Summary

Title / Description	Complex map of the inverse Tania function, ${\displaystyle y=\mathrm {ArcTania} (x)}$.
Citizendium author & Copyright holder	Copyright © Dmitrii Kouznetsov. See below for licence/re-use information.
Date created	2011 September 25
Country of first publication	Japan
Notes	For the generation
Other versions	http://tori.ils.uec.ac.jp/TORI/index.php/File:ArcTaniaMap.png
Using this image on CZ	Please click here to add the credit line, then copy the code below to add this image to a Citizendium article, changing the size, alignment, and caption as necessary. {{Image|ArcTaniaMap70.png|right|350px|Add image caption here.}}

Licensing

   

This media, ArcTaniaMap70.png, is licenced under the Creative Commons Attribution 3.0 Unported License

You are free: To Share — To copy, distribute and transmit the work; To Remix — To adapt the work.
Under the following conditions: Attribution — You must attribute the work in the manner specified by the author or licensor (but not in any way that suggests that they endorse you or your use of the work).
For any reuse or distribution, you must make clear to others the licence terms of this work (the best way to do this is with a link to this licence's web page). Any of the above conditions can be waived if you get permission from the copyright holder. Nothing in this licence impairs or restricts the author's moral rights.
Read the full licence.

Generation

The curves are generated with the C++ code below.

The resulting file is used by the Latex document.

The result of compilation of the Latex source can be converted to the *.png or any other format.

C++ generator of curces

For the compilation, files ado.cin and conto.cin should be loaded in the working directory.

#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#define DB double
#define DO(x,y) for(x=0;x<y;x++)
using namespace std;
#include <complex>
typedef complex<double> z_type;
#define Re(x) x.real()
#define Im(x) x.imag()
#define I z_type(0.,1.)
#include "conto.cin"

z_type ArcTania(z_type z) {return z + log(z) - 1. ;}

main(){ int j,k,m,n; DB x,y, p,q, t; z_type z,c,d;
int M=160,M1=M+1;
int N=161,N1=N+1;
DB X[M1],Y[N1], g[M1*N1],f[M1*N1], w[M1*N1]; // w is working array.
char v[M1*N1]; // v is working array
FILE *o;o=fopen("arctaniamap.eps","w");ado(o,162,162);
fprintf(o,"81 81 translate\n 10 10 scale\n");
DO(m,M1) X[m]=-8.+.1*(m);
DO(n,80)Y[n]=-8.+.1*n;
       Y[80]=-.033;
       Y[81]= .033;
for(n=82;n<N1;n++) Y[n]=-8.+.1*(n-1.);
for(m=-8;m<9;m++){if(m==0){M(m,-8.5)L(m,8.5)} else{M(m,-8)L(m,8)}}
for(n=-8;n<9;n++){     M(  -8,n)L(8,n)}
fprintf(o,".0009 W 0 0 0 RGB S\n");
DO(m,M1)DO(n,N1){g[m*N1+n]=9999; f[m*N1+n]=9999;}
DO(m,M1){x=X[m]; //printf("%5.2f\n",x);
DO(n,N1){y=Y[n]; z=z_type(x,y);
       c=ArcTania(z);
      p=Re(c);q=Im(c);
      if(p>-99. && p<99. && q>-99. && q<99. )  {g[m*N1+n]=p;f[m*N1+n]=q;}
         }}
fprintf(o,"1 setlinejoin 2 setlinecap\n"); p=1.8;q=.7;
//p=2;q=1;
for(m=-11;m<11;m++)for(n=2;n<10;n+=2)conto(o,f,w,v,X,Y,M,N,(m+.1*n),-q, q); fprintf(o,".011 W 0 .6 0$
for(m=0;m<10;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N,-(m+.1*n),-q, q); fprintf(o,".011 W .9 0 0$
for(m=0;m<10;m++) for(n=2;n<10;n+=2)conto(o,g,w,v,X,Y,M,N, (m+.1*n),-q, q); fprintf(o,".011 W 0 0 .9$
for(m=1;m<11;m++)  conto(o,f,w,v,X,Y,M,N, (0.-m),-p,p); fprintf(o,".05 W .9 0 0 RGB S\n");
for(m=1;m<11;m++)  conto(o,f,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".05 W 0 0 .9 RGB S\n");
                conto(o,f,w,v,X,Y,M,N, (0.  ),-p,p); fprintf(o,".05 W .6 0 .6 RGB S\n");
for(m=-9;m<10;m++) conto(o,g,w,v,X,Y,M,N, (0.+m),-p,p); fprintf(o,".05 W 0 0 0 RGB S\n");
y= 0.; for(m=0;m<80;m+=4) {x=-7.95+.1*m; M(x,y) L(x+.05,y)} fprintf(o,".07 W 1 .5 0 RGB S\n");
y= 0.; for(m=2;m<80;m+=4) {x=-7.95+.1*m; M(x,y) L(x+.05,y)} fprintf(o,".07 W 0 .5 1 RGB S\n");
fprintf(o,"showpage\n%c%cTrailer",'%','%'); fclose(o);
      system("epstopdf arctaniamap.eps");
      system(    "open arctaniamap.pdf");
      getchar(); system("killall Preview");//for mac
}

Latex document for labels

% Gerenator of ArcTaniaMap.png % Copyleft 2011 by Dmitrii Kouznetsov
\documentclass[12pt]{article} 
\usepackage{geometry} 
\usepackage{graphicx} 
\usepackage{rotating} 
\paperwidth 854pt 
\paperheight 844pt 
\topmargin -96pt 
\oddsidemargin -98pt 
\textwidth 1100pt 
\textheight 1100pt 
\pagestyle {empty} 
\newcommand \sx {\scalebox} 
\newcommand \rot {\begin{rotate}} 
\newcommand \ero {\end{rotate}} 
\newcommand \ing {\includegraphics} 
\begin{document} 
\sx{5}{ \begin{picture}(164,165) 
\put(6,5){\ing{arctaniamap}} 
\put(2,162){\sx{.7}{$y$}} 
\put(2,144){\sx{.6}{$6$}} 
\put(2,124){\sx{.6}{$4$}} 
\put(2,104){\sx{.6}{$2$}}  
%\put(23,100){\sx{.8}{$u\!=\!0$}} 
\put(2, 84){\sx{.6}{$0$}} 
\put(59,85){\sx{.6}{\bf cut}}  
% \put(20, 84){\sx{.8}{$v\!=\!0$}} 
\put(-3,64){\sx{.6}{$-2$}} 
\put(-3,44){\sx{.6}{$-4$}} 
\put(-3,24){\sx{.6}{$-6$}} 
\put( 22,0){\sx{.6}{$-6$}} 
\put( 42,0){\sx{.6}{$-4$}} 
\put( 62,0){\sx{.6}{$-2$}} 
\put( 86,0){\sx{.6}{$0$}} 
\put(106,0){\sx{.6}{$2$}} 
\put(126,0){\sx{.6}{$4$}} 
\put(146,0){\sx{.6}{$6$}} 
\put(164,0){\sx{.7}{$x$}} 
\put( 81, 23){\rot{81}\sx{.8}{$u\!=\!0$}\ero}
\put( 92, 23){\rot{82}\sx{.8}{$u\!=\!1$}\ero}
\put(101, 22){\rot{82}\sx{.8}{$u\!=\!2$}\ero}
\put(111, 21){\rot{83}\sx{.8}{$u\!=\!3$}\ero}
\put(120, 21){\rot{84}\sx{.8}{$u\!=\!4$}\ero}
\put(139,155){\rot{4}\sx{.8}{$v\!=\!8$}\ero}
\put(138,146){\rot{4}\sx{.8}{$v\!=\!7$}\ero}
\put(138,136){\rot{4}\sx{.8}{$v\!=\!6$}\ero}
\put(138,127){\rot{4}\sx{.8}{$v\!=\!5$}\ero}
\put(137,118){\rot{4}\sx{.8}{$v\!=\!4$}\ero}
\put(136,109){\rot{4}\sx{.8}{$v\!=\!3$}\ero}
\put(135,100){\rot{4}\sx{.8}{$v\!=\!2$}\ero}
\put(134, 92){\rot{3}\sx{.8}{$v\!=\!1$}\ero}
\put(134, 84){\rot{0}\sx{.8}{$v\!=\!0$}\ero}
\put(134, 76){\rot{-3}\sx{.8}{$v\!=\!-\!1$}\ero}
\put(133, 68){\rot{-5}\sx{.8}{$v\!=\!-\!2$}\ero}
\put(134, 59){\rot{-5}\sx{.8}{$v\!=\!-\!3$}\ero}
\put(135, 51){\rot{-5}\sx{.8}{$v\!=\!-\!4$}\ero}
\put(135, 41){\rot{-5}\sx{.8}{$v\!=\!-\!5$}\ero}
\put(135, 32){\rot{-5}\sx{.8}{$v\!=\!-\!6$}\ero}
\put(136, 23){\rot{-5}\sx{.8}{$v\!=\!-\!7$}\ero}
\put(137, 14){\rot{-5}\sx{.8}{$v\!=\!-\!8$}\ero}
\end{picture} 
} 
\end{document}

%Use for free, attribute the source. This is not for any kind of priority; this is to trace the errors if any.